A topological Josephson traveling wave parametric amplifier

We show how to realize a topological traveling wave parametric amplifier with a chain of Josephson junctions and four-wave mixing. The amplifier manifests directional and near quantum-limited amplification of microwave signals with a gain that grows exponentially with the chain size while keeping the bandwidth constant. We show that the directional amplification has a topological origin and therefore does not require any engineering to maintain phase matching along the chain, and it is moreover resilient to disorder. This Josephson topological amplifier can be immediately implemented with state-of-the-art superconducting technology, opening up a new route for the efficient detection of microwave quantum signals.